Somone suggested that bringing in a social worker may be helpful in the situation with my aunt.

I'm curious about what a social worker can DO with someone who has dementia symptoms (won't leave the house, even to visit a doctor) but is very proud and knows how to strongly express that she is fully capable and independent.

If I recall correctly, a social worker cannot get the power to do anything against her will such as moving her to assisted living/nursing home - unless she is a danger to herself or others?

For example, if she expresses that any medical care and her living necessities - or lack thereof - is her business and that she doesn't need anyone's intrusion into her life - what can a social worker actually do?

Would bringing a social worker over to speak to her cover any legal liability for me in the case that something should happen to her health-wise while I was staying at her home (unoficially) to assist her with daily living?

If a social worker visits and sees that a person cannot care for themselves, they can intervene. BUT, if someone isn't incompetent, they can do nothing to force them to get treatment or assistance.

Your best bet is to go speak with a social worker yourself and ask them what, in your state, can be done to help encourage a relative to allow themselves the care they need.

I know this is going to vary depending on where you live, but generally speaking does a social worker catch dementia symptoms - e.g. lack of short term memory - in their test for competency?

I'm sure they are aware of office tests, etc., but their job isn't to diagnose - it it to ascertain the level of a person's ability to conduct their ADLs without assistance. If they cannot do so, they can make suggestions on how/where to seek assistance. If they do a home visit and find someone in a dangerous or totally unacceptable condition, they can take steps to see that the person is protected.

To find out what they can and cannot do, why not call and discuss the situation with them anonymously?